Finding and only finding local Nash equilibria by both pretending to be a follower

Xuchan Bao, Guodong Zhang

Keywords: game theory, general-sum games, local Nash equilibrium, optimization

TL;DR: We propose double Follow-the-Ridge (double-FTR), an algorithm with local convergence guarantee to differential Nash equilibria in general-sum two-player differential games.

Abstract:

Finding (local) Nash equilibria in two-player differentiable games is a classical problem in game theory with important relevance in machine learning. We propose double Follow-the-Ridge (double-FTR), an algorithm that locally converges to and only to local Nash equilibria in general-sum two-player differentiable games. To our knowledge, double-FTR is the first algorithm with such guarantees for general-sum games. Furthermore, we show that by varying its preconditioner, double-FTR leads to a broader family of algorithms with the same convergence guarantee. In addition, double-FTR avoids oscillation near equilibria due to the real-eigenvalues of its Jacobian at fixed points.
Empirically, we validate the double-FTR algorithm on a range of simple zero-sum and general sum games, as well as simple Generative Adversarial Network (GAN) tasks.

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